A column generation and branch-and-cut algorithm for the channel assignment problem

  • Authors:

  • Têkogan D. Hemazro;Brigitte Jaumard;Odile Marcotte

  • Affiliations:

  • Department of Electrical Engineering, ícole Polytechnique de Montréal, P.O. Box 6079, Station Centre-ville, Montreal (Quebec), Canada H3C 3A7;Concordia Institute for Information Systems Engineering, Concordia University, 1455 de Maisonneuve Blvd. W., Montreal (Quebec), Canada H3G 1M8;Department of Computer Science, Université du Québec í Montréal, P.O. Box 8888, Station Centre-ville, Montreal (Quebec), Canada H3C 3P8

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2008

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Abstract

We present an exact algorithm for solving the channel assignment problem in cellular telephony networks. This problem consists of assigning sets of channels to the network cells in such a way that the channel demand is satisfied, while avoiding co-channel interference and adjacent channel interference and respecting the channel spacing constraint for each antenna. In a previous article [Jaumard B, Marcotte O, Meyer C, Vovor T. Comparison of column generation models for channel assignment in cellular networks. Discrete Applied Mathematics 2002; 118:299-322], we formulated this problem as a covering problem in two different ways and compared these two formulations and another formulation both from a theoretical and computational point of view (by solving their linear relaxations). In the present article we focus on the best set covering formulation, where the subsets are sets of cells that can be assigned the same channel, and we actually solve two versions of the integer program. In the first version, we seek to minimize the unmet demand, while in the second, we seek to minimize the overall interference while assigning the required number of channels to each cell. In either version, the integer program is solved by an algorithm combining the column generation technique and a branch-and-cut scheme. Finally, we present the solutions produced by these algorithms for some instances of European networks and real-life instances supplied by the Bell Mobilité company.